Higher Education · Numerical Methods
Numerical Integration
What is it
Numerical integration estimates the value of a definite integral when an exact antiderivative can't be found, using methods like the trapezium rule and Simpson's rule that approximate the area under a curve using simple shapes.
Why it matters
Most real-world functions — especially those derived from measured data rather than clean formulas — can't be integrated exactly, making numerical integration the only practical way to calculate areas, volumes, and accumulated quantities in applied work.
Exam tip
Simpson's rule is generally far more accurate than the trapezium rule for the same number of points, since it fits parabolas rather than straight lines — use Simpson's rule by default unless a specific reason favours the trapezium rule.
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